Sheff Posted October 14, 2016 Share Posted October 14, 2016 I am aware a set is Bounded if it has both upper and Lower bound and i know what a Limit point of a set is but how can i show that If S ⊂ R be a "bounded infinite set", then S' ≠∅ Link to comment Share on other sites More sharing options...
fiveworlds Posted October 14, 2016 Share Posted October 14, 2016 A "bounded infinite set" is a discrete (finite) subset of an infinite set as opposed to a discrete subset of a discrete set. Eg finite set {alphabet} discrete subset {letters a - g} infinite set {integers} discrete subset {0 - 20} Link to comment Share on other sites More sharing options...
studiot Posted October 14, 2016 Share Posted October 14, 2016 A "bounded infinite set" is a discrete (finite) subset of an infinite set as opposed to a discrete subset of a discrete set. Eg finite set {alphabet} discrete subset {letters a - g} infinite set {integers} discrete subset {0 - 20} Careful here. Both the sets [0,1] and (0,1) are infinite bounded subsets of R. The question is surely fairly trivial since R is unbounded (1) So partitioning R into subsets S and S' where S' is the null set and S is R is contradicts (1) Sheff, Is this homework??? I will leave you to finish off formally, moderators may move this to the homework section. 1 Link to comment Share on other sites More sharing options...
Sheff Posted October 14, 2016 Author Share Posted October 14, 2016 Yea this is a homework bro which i must turn in on Monday. Thanks for the Insights. Link to comment Share on other sites More sharing options...
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